The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  1  1  1  0  X  1  1  1  1  1  1  0 2X  1  1  1  1  1  1  0 2X  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1  0 2X  1  1  1  0  1  1  1  1  1  1  1  X  X  1  X  1  0  0  1  1  1  1  1  1  1  1  1  1  1  X  1  1 2X  X  1 2X  1  X
 0  1  1  2  0  1  2  1  0 2X+1  2  1  0 X+1 X+2  1  1  0 2X+1  2 2X+2 X+1  X  1  1  X 2X+1  2  0 X+2  1  1  1  2 2X+1 2X  2  1 2X+1  2 2X+1  X X+2  0  1 2X+2 2X 2X+1 2X 2X  1  1 2X+2  0 X+1  1 X+2 2X X+2 X+2 X+1 2X X+2  1  1  0  1  2  1  1  0  1 2X X+2 X+1  1 2X+2  2 X+1 2X  2  1  X  2  1  0 X+1  1  0 2X
 0  0 2X  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X 2X  X 2X  X  X  X  X  X 2X 2X  X  0 2X  0  X  0  X  X  X  0  X 2X 2X 2X  X 2X  0 2X  X  0  0 2X 2X 2X 2X  0  0 2X 2X  X  X 2X 2X  0  0 2X 2X  X 2X  0  0  X 2X 2X  X 2X 2X  0  0  X 2X  X  X  0  X  0  X  X  0  0 2X  X
 0  0  0  X  0  0  0  0  0  0  0 2X  0  0 2X  X 2X  0 2X 2X  X  X  0  X  0  0 2X  X 2X 2X  X  X 2X  X  0  0  X 2X  X  0 2X 2X 2X 2X  X 2X  0 2X  0  X 2X  X  0  X  0  X  X  X  0  0 2X  X 2X 2X  X  0 2X 2X  0  0  X  0  X  0  0  0  X  0 2X  X  0  X  X  X  X  0 2X  X 2X  0
 0  0  0  0  X  0  0  0  X 2X 2X  0  X 2X 2X  X 2X  X  X 2X  0  X 2X  0 2X  X 2X 2X 2X  X  0  0  0  0 2X  X  0 2X  0  X  X 2X  0 2X  0  0 2X  X  X 2X 2X 2X 2X 2X  X  X  X  X  X  X  0 2X 2X  0  X  0  X  0 2X  0  X  X  X 2X  0 2X  0  0  0  0  0  X  X 2X 2X  0  0  0  0  X
 0  0  0  0  0 2X  0  X 2X 2X 2X 2X  0  X 2X  0  X  0 2X 2X  0 2X 2X  0  0  0  X 2X  0  X  0  X  0  X 2X 2X  X  0  0  X  X  0 2X  X  0 2X  0  0  0  X 2X 2X 2X 2X 2X 2X 2X  X 2X  0  0  0  X 2X 2X  X  X  0  0  X  0 2X 2X  0  X 2X  0  X  0 2X 2X 2X  0  X  0 2X  X 2X  X  X
 0  0  0  0  0  0  X 2X 2X 2X  0 2X 2X 2X  X  0 2X  X  0  X  0 2X  0  X  X  0  X  0 2X  X  X 2X  X  0  X  0  0 2X  0  X 2X  X 2X 2X  X  X  X  0  X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0  X  0  0  X 2X 2X  X  0 2X 2X  0  0  X  X  X  0  X  0 2X  0  0  X  0  0  0  X  0 2X 2X  X

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+170x^162+30x^163+90x^164+286x^165+132x^166+144x^167+592x^168+312x^169+390x^170+996x^171+378x^172+420x^173+1196x^174+564x^175+546x^176+1466x^177+552x^178+702x^179+1660x^180+744x^181+600x^182+1494x^183+672x^184+600x^185+1296x^186+444x^187+450x^188+878x^189+354x^190+294x^191+378x^192+144x^193+114x^194+198x^195+42x^196+24x^197+108x^198+6x^199+70x^201+52x^204+38x^207+30x^210+12x^213+10x^216+2x^219+2x^222

The gray image is a linear code over GF(3) with n=270, k=9 and d=162.
This code was found by Heurico 1.16 in 30.8 seconds.